Treatment simulator for brain diseases and method of use thereof

ABSTRACT

A treatment simulator for providing information on physiological states and effects of treatment of neurological disease, comprising a computer, and an application configured to operate with the computer. The application is capable of: obtaining radiological imaging from the brain; obtaining anatomical information from the radiological imaging within a region of interest within the brain; constructing a physiological states model which assesses physiological states of the region of interest; locating sources of interstitial flow of particulate matter and obtaining fluid conductivities of paths of the interstitial flow utilizing the anatomical information and the physiological states model; and creating a flow model of the particulate matter which assesses velocities of flow and interstitial pressure variations utilizing the sources of interstitial flow and the fluid conductivities.

This application is a Divisional of U.S. patent application Ser. No.12/116,765 filed May 7, 2008, which claims priority to U.S. ProvisionalPatent Application No. 60/938,863, filed on May 18, 2007, and entitled“A Treatment Simulator For Brain Diseases And Method Of Use Thereof”.All of the foregoing are incorporated by reference in their entireties.

FIELD OF THE INVENTION

The present invention relates to the field of physiology, diagnostics,monitoring, and treatment.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates a flow model for assessing velocities of flow andinterstitial pressure variations, according to one embodiment.

FIGS. 1A-1B illustrate pressures and velocities used in an example of aflow model construction, according to one embodiment.

FIG. 1C-1D illustrate a system for providing information for treatingbrain disease, according to one embodiment.

FIG. 1E illustrates various treatment plans for brain disease, accordingto several embodiments.

FIGS. 2-10 illustrate various methods of providing information fortreating brain disease, according several embodiments.

FIGS. 11-12 illustrate behaviors that affect a user interface utilizedfor providing information for treating brain disease, according toseveral embodiments.

FIG. 13-14 illustrate screen shots that can be used in the system andmethod, according to several embodiments.

DETAILED DESCRIPTION OF THE EMBODIMENTS OF THE INVENTION

A system and method is illustrated for providing more information at thepoint of care for effective planning and dispensation of treatment forbrain diseases. The pathways into the brain are often the paths ofingress of chemotherapeutic molecules entering the brain, as well as thepaths of egress of such molecules leaving the region in the brain wherethey are needed. Likewise, the pathways within the brain are the routesof migration of primary brain cancer cells, of advection of plaque inAlzheimer's disease, of serum proteins from disrupted blood-brainbarrier in diseases, of endogenous flow dictating the long termmigration of therapeutic particles, and other important phenomena inhealth and sickness. Information on these pathways and their functionhelp in a variety of brain disorders, and also help estimate howchemotherapeutic and other particles distribute from, and along, thesepathways.

System for Treating Brain Disease

FIG. 1C illustrates a system for treating brain disease, according toone embodiment. Client computer 1 is connected to server computer 2 by anetwork. Server computer 2 has an application 3 which helps provideinformation to treat brain disease. Note that, in one embodiment,application 3 is part of or connected to server computer 2. However, insome embodiments, application 3 may be connected to server 2 by thenetwork.

FIG. 1D illustrates details of how application 3 functions, according toone embodiment. Radiological imaging is collected on a patient using aradiological imaging system 5. Possible radiological imaging systems caninclude MRI, positron emission tomography (PET), imaging of radioactivelabels in chemotherapeutic molecules, CT, etc. A raw signal recorder 4can record the raw signals available from the radiological imagingsystem 5 so that the raw signals can be reconstructed by an imagereconstruction system 6 and put to use. This is optional and can improvethe performance of the system in some embodiments, but is not necessary.The algorithms 7 can be reduced to software and compiled or interpretedon the host computer and thus can run on the radiological imaging data.The host computer 8, can be a computer associated with the imagingsystem itself, a laptop, the workstation in the physician's office, oreven computers in a remote location (e.g., used when the work isoutsourced). The computer 8 can have interface 9, storage, 10 and printcapabilities 11. Retrospective data 12, such as individual patientrelevant clinical records, other imaging data, or statistical datacollected on similar patients, etc., can also be utilized by thecomputer 8, in some embodiments. The user interfaces 15 and displays 14of models can then be used by appropriate users (e.g., specialists).

Treatment of Brain Disease

FIG. 1E describes various treatment plans of brain disease, according toseveral embodiments of the invention. The top row illustrates theassessment needs for four example decision routes that physicians chooseamongst, namely surgery, radiation therapy, chemotherapies following anassessment of the state of a cancer (oncological), and ancillarytherapies, such as steroid treatments. New assessments can be made thatcan modify decision routes, both in terms of their timing and theirextent. Examples of these are described for each of the decision groupsbelow. Those of ordinary skill in the art will see that many otherdecision routes and assessments can be made.

Surgery.

Neurosurgeons can use the history, physical examination, andconventional information from magnetic resonance imaging (MRI) scans todetermine the location, contrast enhancement, amount of edema and masseffect to decide on their surgical procedure. Information can also beprovided on high risk recurrence zones, likely toxicities of surgery,and likely patterns of spread that is not conventionally available. Thiscan shape their decisions on how to approach surgery and whether localtherapies should be considered intraoperatively.

Radiation.

Radiation oncologists can use the history, physical examination, andconventional information from MRI scans to determine the location,contrast enhancement, amount of edema and mass effect to decide on theirplanned radiation therapy. Information can also be provided on high riskrecurrence zones, likely toxicities of radiation therapy, and likelypatterns of spread that is not conventionally available. This can shapetheir decisions on how to design their overall radiation fields andtheir decisions on the region to boost with additional external beam orinterstitial radiation.

Medical Oncology.

Medical oncologists can use the history, physical examination, andconventional information from MRI scans to determine the dimensions of acontrast enhancing tumor and the amount of edema and mass effect inplanning permeability and drug distribution maps based on: 1) the agent(e.g., molecular weight and lipid solubility), 2) route of delivery(e.g., systemic [e.g., intravenous or intraarterial] or interstitial[e.g., convection enhanced delivery (CED) or polymeric delivery]), and3) potential changes to the integrity of the blood brain barrier (BBB)(e.g., change in steroids, post-RT, intra-arterial mannitol, etc). Thisphysiologic information can affect clinical decisions on the use ofpharmacologic agents in these diseases.

Ancillary Therapies.

Steroids, such as glucocorticoids, can be used as therapy forperitumoral brain edema and work by altering the integrity of the bloodbrain barrier. If the BBB is markedly disrupted, large amounts of plasmaproteins enter the brain osmotically bringing water with them. Thiscauses an increase in the flow of fluids down white matter tracts whichmay further disseminate these tumors with the central nervous system. Inaddition, once these white matter tracts are overloaded, extracellularfluid backs up in the region of the leaky BBB causing mass effect,increased Intra-Cerebral Pressure (ICP) and symptomatic deterioration.While high doses of glucocorticoids would be advantageous for thereasons listed above, they can cause serious systemic toxicities.Physiologic parameters can provide unique information to make rationaledecisions to minimize steroid doses (such as glococorticoids) whilemonitoring WMT flow rates and amounts of edema, potentially reducing theintracranial dissemination of these cancers.

Another example of an ancillary therapy is plaque dissolving therapy.Alzheimer's disease is one where plaque can form in the neocortex, dueto clumping of the mutated amyloid beta protein. The nearest CerebralSpinal Fluid (CSF) spaces tend to be the perivascular or Virchow-Robinspaces, and thus the flow of interstitial fluid here tends to accumulatethe plaque in these spaces. A map of the fluid pathways that are in thecortex can give the physician the most likely points of accumulation ofplaque, and thus the target regions for plaque-dissolving therapies.

Other ancillary therapies that can be used include the distribution ofcytokines for directing stem cell migration in brain parenchyma, and asimulator for drug delivery for pharmaceutical industry applications.Some examples of these will be described in further detail below.

Construction of the Treatment Simulator

One component of a treatment simulator is the construction andembodiment of a model for endogenous flow of interstitial fluid (ISF) inthe brain. FIG. 1 illustrates the basics in the construction of such aflow model, which assists in therapeutic decisions as described in FIG.1, according to one embodiment. First, one or more radiological imagesare taken (105). These include but are not limited to diffusion tensorimaging with for example, a so-called {tilde over (b)} value of 1000that allows us to delineate the directionality of the white matter fibertracts; and a T1-weighted SPGR (spin spoiled gradient recalled echosequence) proton density imaging protocol and/or a dual-echo T2 weightedimage for the same purpose. (These acronyms are well known in the fieldof magnetic resonance (MR) imaging.) In combination with the diffusiontensor image, this allows us to construct a map of the extracellularvolume fraction, which is of particular interest in brains with injurysuch as trauma, or stroke, or disease, such as brain cancer, orAlzheimer's. Further imaging that could be taken include dynamiccontrast enhanced (DCE) imaging with either MR or CT (computedtomography) visible contrast agents that allow us to construct maps of(i) the plasma fluid filtration rate, (ii) the capillary density or(iii) the BBB permeability to water-soluble molecules of size similar tothat of the contrast agent used. The filtration rate and the capillarydensity allow us to construct both a source strength and source densityfor endogenous fluid flow in the brain. Thus from these and otherimages, we can deduce the physiological parameters (115) and theirspatial locations (overlay with 110) that provide the constitutive andsource terms in a mathematical model for bulk flow of interstitial fluidin the brain (120). In 125, the mathematical model computes theintracranial pressure distribution and the fluid flow pathways andvelocities from a combination of D'Arcy's law for fluid flow in a porousmedium and the conservation of mass of fluid (allowing for the capillarysources including ones that arise on account of the damaged BBB inbrains with disease or injury). In 140, the model flow is obtained. Thisis discussed in more detail below.

In one embodiment, direct experimental construction of bulk flowpathways in an individual brain can be provided (130, 134, 138). In 130,a magnetic resonance contrast agent such as beads encapsulated with ironparticles, or emulsion particles with a coating of Gadolinium (thoseskilled in the art will know of other possibilities, as well as use ofother imaging modalities, such as the use of contrast reagents forcomputed tomography (CT) can be deposited at particular parts of thebrain, and tracked for periods of time. In 134, by suitable choice ofsize of particles, and of the magnetic moment encapsulated within ordistributed on the surface, one can map the flow velocities whichconvect the beads, without the confounding issue of diffusive or othertransport. In 138, such experimental construction can also be used toimprove, refine, or update the flow model. We now describe below anapproach to the construction of the mathematical model mentioned in thepreceding paragraph.

Mathematical Model for Bulk Flow.

Herein, we describe some mathematical approaches to modeling the bulkflow pathways, and for obtaining the patient-specific parameters toimplement the model for a particular living brain. Since theconcentrations of various types of particles will be referred to, wesummarize our notation:

Symbol for particle concentration Particle type c Serum proteins,principally albumin m Contrast reagent for perfusion imaging nChemotherapeutic molecule

In a normally functioning, intact brain there is production and removalof interstitial fluid. It is generally agreed that the sources of fluidare the vasculature and capillaries. The sinks are the CSF spaces (e.g.,the ventricles, the perivascular, and the periarterial spaces). Theadditional fluid pumped into the brain due to a growing tumor and theattendant edema can have importance in tumor migration.

The source of interstitial fluid is generally accepted to be thecapillary system in the brain. Kinetic equations for transport across amembrane yield a production rate for fluid per unit volume of tissueaccording to

$\begin{matrix}{{\nabla{\cdot v_{i}}} = {q:={\frac{L_{p}S}{V}\left( {\left( {p_{v} - {R\; \Pi_{v}}} \right) - \left( {p - {R\; \Pi}} \right)} \right)}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

Note that := means that the quantity facing the colon is defined to bethe quantity facing the equality sign.

$\frac{L_{p}S}{V}$

is the capillary hydraulic conductivity per unit tissue volume. Thev_(i) is the interstitial velocity. The p's are hydrostatic pressuresinside the capillaries (subscript v)) or in the interstitial space (nosubscript). The q is the interstitial production rate. The Π are thecorresponding osmotic pressures of blood plasma proteins (e.g.,albumin). R is called the osmotic reflection coefficient¹ and has amicroscopic interpretation that relates it to the equilibrium albuminconcentrations inside and outside the vessel. Phenomenologically, Rmeasures the departure of the vessel walls from semi permeability withR=1 being impenetrable to the albumin or solute in question, and R=0being open to the diffusive transport of both solute and solventmolecules. Active transport of molecules across the wall as well astransport of ions with the accompanying electrical phenomena such asvoltages across the membrane will require further considerations.Equation (1) can be combined with D'Arcy's law, extended to includeosmotic pressure

v _(i) =−K∇(p−Π)  (Equation 2)

so that we may begin to discuss how to solve for the bulk flow pathways.(Note that K is the hydraulic conductivity.) Substituting from D'Arcy'slaw into Equation (1) results in one equation for two unknown functionsof space: p and Π. ¹It is usually denoted by σ but we reserve thisletter for the Cauchy stress.

Endogenous Bulk Flow in Normal Brain.

Let us consider a normal, intact brain. We can for example take theintravascular pressure, the osmotic pressures, the hydraulic conductanceof the capillary wall, and the reflection coefficient to all be fairlyuniform. The intravascular pressures can range from an average of closeto 100 mm of Hg in the middle cerebral artery down to below 20 mm in thearterial capillaries. Below, for purely illustrative purposes, we willassume a uniform distribution of the capillaries per unit volume oftissue as well. Later we describe how to obtain this and otherparameters specific to an individual to construct an individualized bulkflow map. The right hand side of Equation (1) must be positive for thereto be an influx of fluid from blood vessels to the interstitium.

Illustrative Analytic Examples.

Let us first consider a homogeneous, isotropic, spherical brain. Weregard the outer surface of the brain to be a sphere of radius b, whilethe ventricles are considered an inner sphere of radius a<b. Taking allparameters to be homogeneous and isotropic, so that in particular thetensor field of the hydraulic conductivity is a single number k, we getfrom D'Arcy's law,

$\begin{matrix}{{\nabla^{2}p} = {\overset{\sim}{q} = {\text{:}\frac{q}{\varphi \; k}}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

Replacing the Laplacian by the form it takes in radial coordinates r

$\begin{matrix}{{\frac{1}{r^{2}}\frac{}{r}\left( {r^{2}\frac{p}{r}} \right)} = {- \overset{\sim}{q}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

The general solution to this is

$\begin{matrix}{{\frac{p(r)}{c} = {{- \frac{A}{r}} - r^{2} + B}}{\frac{p^{\prime}(r)}{c} = {{- \frac{A}{r^{2}}} - {2\; r}}}{c:=\frac{\overset{\sim}{q}}{6}}} & \left( {{{Equations}\mspace{14mu} 5},\; 6,7} \right)\end{matrix}$

(Note that A and B are constants of integration.) The most naturalboundary condition is to assume that the CSF in the ventricles and inthe sub-arachnoid space is at a constant pressure, which we take to bethe reference or zero pressure:

p(r=a)=0==b)  (Equation 8)

If, however, we assume that the interstitial fluid drainage is allthrough the ventricles and not through the pial surface intosub-arachnoid space, the boundary condition would be of the form

$\begin{matrix}{{\left. v_{r} \right|_{r = a} = {given}}\text{}{{p\left( {r = b} \right)} - 0}} & \left( {{{Equations}\mspace{14mu} 9},10} \right)\end{matrix}$

where v_(r) is the radial influx speed into the ventricles. UsingD'Arcy's law, and again assuming every portion of the inner surface isequally permeable to the fluid, this boundary condition is of the form:

$\begin{matrix}{\left. \frac{p}{r} \right|_{r = a} = {\frac{q}{4\; {\pi a}^{2}} \times \frac{1}{\varphi \; k}}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

Choose a=1, b=½√{square root over (217)}−½≈6.865. (These radii will bein rough agreement with the ratio of the ventricular volume to brainvolume. The choice for b can be for convenience.) The two curves inFIGS. 1A and 1B show the behaviors of the pressures and the velocitiesfor the two different boundary conditions we have indicated. The largerpressure variations occur for the model where the flux is forced to beentirely into the ‘ventricular’ space in this model. Note that FIG. 1Aillustrates pressures with different boundary conditions. FIG. 1Billustrates velocities (positives=radially inward).

Returning to computing the bulk flow pathways, we can do so provided wehave an estimate for q, the interstitial production rate, as well as thehydraulic conductivity K over the region of the brain. This is becausewe are on fairly sure ground in assuming a uniform background ofsources, in proportion to the specific volume of the functioningcapillaries. We discuss obtaining these parameters later, and proceedwith the case of brains with injury that results in edema, and abreakdown of the BBB.

Bulk Flow Pathways in Edematous Brain.

As a prelude to discussing methods we could apply to an individualizedbrain, let us revisit the equations, but this time for a brain wherethere are disruptions of the BBB. In this case, at a minimum, we cannotneglect the variations of the reflection coefficient and theinterstitial osmotic pressures. However, in the expression

$\begin{matrix}{q = {\frac{L_{p}S}{V}\left( {\left( {p_{v} - {R\; \Pi_{v}}} \right) - \left( {p - {R\; \Pi}} \right)} \right)}} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

we note the following: q itself may be obtained by certain contrastimaging techniques (see later). For the individual terms, the capillaryconductance does not vary much: the disruption of the BBB is causedmostly due to the increased permeability of the capillary walls to theserum proteins (R≠1 where there is disruption). We need to estimate thisreflection coefficient in different parts of the brain. However, againdue to the capillaries being the primary source, we can assumeapproximately that p_(v)−RΠ_(v) varies primarily due to BBB disruption.However, we need now to account for the fact that the albumin hasdistributed over the interstitial space, having spilled out of regionsof disruption. For this, we invoke the equation of flow of particles inthe interstitial space (see above). Denoting the concentration ofalbumin in the interstitial space by c, and in the blood vessels byc_(v) and accounting for the source which produces this, we have, bymaking the simplification that the convective velocity of the protein inthe interstitium is just that of the fluid,

$\begin{matrix}{{\frac{\partial c}{\partial t} = {{{- \nabla} \cdot ({cv})} + {\nabla{\cdot \left( {D\; {\nabla\; c}} \right)}} + q_{c} - {a\left( {c,p} \right)}}}{q_{c} = {{\frac{PS}{V}\left( {c_{v} - c} \right)} + {{q\left( {1 - R} \right)}c_{v}}}}} & \left( {{{Equations}\mspace{14mu} 13},14} \right)\end{matrix}$

Note that t is time, and a(c, p) is a term that accounts for chemicalreactions and metabolism. The expression for the transport of the soluteinto the interstitial space (Equation 14) is standard, but is somewhatsimplified in the last term, where more nonlinear terms could be takeninto account. Further, as the references show, it is a simplification toidentify R with the osmotic reflection coefficient previouslyintroduced. It can be more correctly identified with a differentparameter called the solute drag coefficient or ultrafiltrationcoefficient. Mindful of the need for perhaps taking into account thesemore accurate theories, we proceed by using the simpler case as theexemplar. Substituting for ∇·v from above, we get (only the case R≠1 isrelevant for our example purposes)

$\begin{matrix}{\frac{\partial c}{\partial t} = {{{- v} \cdot {\nabla c}} + {\nabla{\cdot \left( {D\; {\nabla c}} \right)}} + {\left( {\frac{PS}{V} + q} \right)\left( {c_{v} - c} \right)} - {Rqc}_{v} - {k_{d}c}}} & \left( {{Equation}\mspace{14mu} 15} \right)\end{matrix}$

where we have replaced the complex biochemistry for albumin in brainparenchyma by an irreversible degradation rate, which is known fromvarious studies. Note that k_(d) is the degradation and loss of serumprotein from interstitium. We need to solve the equation for the ρ, Πsimultaneously to derive the bulk flow pathways. The osmotic pressure isa defined function of the interstitial concentration, in the dilutelimit it is just

Π=kTc  (Equation 16)

where the concentration is the number of molecules per unit interstitialvolume. (Note that T=temperature; k=Boltzmann's constant, and c=theconcentration of serum protein in interstitium.) More exact expressionscan be used if found necessary. Assuming we know the parameters (e.g.,the hydraulic conductivity, functional capillary density, diffusivity,permeability, reflection coefficient, and degradation rate) we canreduce the pair of equations to completion, if we know p_(v) and Π_(v).We can assume these to be fairly constant. Then, we have a pair ofpartial differential equations, equations (1) and (15), that need to besolved simultaneously. We have displayed only the steady-state equationfor the fluid velocity; since in many circumstances we encounter thebrain somewhat after disease, such as when cancer has taken hold, andthe period of our observation can be fairly short, we can also look justat the steady state version of the concentration equation where theright hand side of (Equation 13) can be set to zero. The boundaryconditions on the hydrostatic pressure are given at the interfacesbetween the parenchyma and the cerebrospical fluid (the ventricles andthe arachnoid granulations), reducing to the measurable and known CSFpressure there. The initial/boundary conditions on the albuminconcentration flux can be assumed to be proportional to the

$\frac{PS}{V},$

or to

${\frac{PS}{V} + q},$

and to go to zero at me outer edges due to reabsorption and degradation.This then is an approach to solving for the bulk flow pathways in thepresence of edema and disease. A review of the approaches to theparameter estimation is given in that the next section.

Parameter Estimation.

In order to solve the equations for a particular individual, we have toestimate several parameters. We list these in the table below, and thendiscuss the imaging methodologies which allows us to estimate theparameters. All parameters belonging to an imaging methodology arediscussed under that rubric. For brevity, we discuss one method forobtaining each of the parameters: there are other potential methodswhich we do not list or discuss which will be apparent to those ofordinary skill in the art.

Symbol Meaning How obtained φ connected extracellular fluid volumeProton density fraction imaging v fluid velocity field relative totissue Solved via D'Arcy's law q rate of production of interstitialfluid DCE K hydraulic permeability DTI p hydrostatic pressure relativeto a resting Solved for pressure in tissue c concentration of serumprotein in Solved for interstitium Π osmotic pressure of serum proteinin constitutive relation interstitium to c D extracellular diffusiontensor of serum DTI protein in interstitium k_(d) degradation and lossof serum protein from Assumed/estimated interstitium R reflectioncoefficient for serum protein DCE from capillary walls $\frac{PS}{V}$Permeability-area product per unit tissue volume for serum protein DCE$\frac{L_{p}S}{V}$ Capillary hydraulic conductivity DCE

Proton Density Imaging.

We estimate the pore or extracellular volume fraction from protondensities. Proton density or other imaging can give us the waterfraction. To convert the water fraction to an extracellular volumefraction, we need to know the fraction of the volume that containswater. The extracellular volume fraction is arrived at followinganatomic imaging that delineates grey matter, white matter, CSF spaces,etc. and assigning nominal values known from the literature related tothese regions. The proton density image then allows us to compute theextracellular volume by observation of the current proton density.

Perfusion and Dynamic Contrast-Enhanced Imaging (DCE).

All of the parameters obtainable from DCE are done with a time-seriesanalysis following bolus injection. Although, there are many methods forexamining transcapillary transport, for example purposes we focus on MR-and CT-based dynamic contrast enhanced imaging. A two-compartment modelfor DCE imaging models the rate at which the contrast agent (withconcentration here denoted by m for marker) is the short time version ofthe equation used for the albumin concentration above, but withparameters appropriate to the contrast agent:

$\begin{matrix}{{\varphi \frac{m}{t}} = {{\frac{{PS}_{m}}{V}\left( {m_{v} - m} \right)} + {{q\left( {1 - R_{m}} \right)}m_{v}}}} & \left( {{Equation}\mspace{14mu} 19} \right)\end{matrix}$

where m is the interstitial concentration of the tracer, PS_(m) is thepermeability-area product per unit tissue volume of the blood vessels tothe tracer, R_(m) is the reflection coefficient discussed above, but nowfor the tracer molecule (the suffix is appropriate when it is aGadolinium chelate), and m_(v) is the concentration of the tracermolecule within the blood vessels. q has exactly the same meaning asabove, namely the rate per unit tissue volume, at which fluid is beingpumped out of the blood vessels into the interstitium in the brain whichhas been invaded by tumor, but not yet by CED interventions. (This iscalled the filtration rate of the plasma fluid.) The first term on theright hand side is the diffusive transport of the tracer, the second theconvective transport. Again this equation applies at every spatiallocation (voxel) in the brain. There is of course a second equation forthe plasma or blood vessel concentration of the contrast agent:

$\begin{matrix}{{\varphi_{v}\frac{m_{v}}{t}} = {{F\left( {m_{A} - m_{v}} \right)} - {\frac{{PS}_{m}}{V}\left( {m_{v} - m} \right)}}} & \left( {{Equation}\mspace{14mu} 20} \right)\end{matrix}$

The variable m_(A) is called the arterial input function, and is eitherknown, or allowed for. F is related to the regional cerebral blood flow.Following an injection of a bolus of the contrast agent by imaging, onecan, from a time-series analysis, fit the parameters to obtain theparameters above, as well as the functional capillary density (relatedto the integrated signal over time) wherever there is signal.

Diffusion Tensor Imaging.

Diffusion tensor imaging can be used in various ways to obtain hydraulicconductivity and the diffusion of large molecules.

In FIG. 2, we show a comprehensive tumor dissemination model, whereindiffusion (including the convective component of diffusion that variesspatially) and proliferation are included to provide a risk map forrecurrence. This map can be overlaid on anatomic, surgical, or radiationtherapy planning maps to provide the physician with further information,as has been discussed in conjunction with FIG. 1 above. In addition tothe bulk flow dissemination of tumors (obtained from 100 as discussedfor FIG. 1), additional information is obtained both from the prior data(e.g., biology) of the tumors (202) which can give indications of theproliferation rate either in-vitro or, from biopsies, a certain amountof in-vivo information can be added. Since biopsies are not routinelyrepeated, estimates from a combination of (i) longitudinal contrastimaging (201) which gives crude estimates of proliferation rates whenthe tumor mass is substantial enough to be visible in contrast-enhanceMR, and (ii) biologic information about the proliferation rate of thetumor cells (202), and (iii) any further quantization obtainable fromestimates of the fraction of tumor stem cells within given masses oftumor (204), can all be used to estimate the proliferation rate in-vivo(203). Further, the different methods will give us quasi-independentestimates which can then be compared for consistency. A model thatcombines bulk flow (100), diffusion (115), and proliferation (203) canthen be constructed, and a patient-specific model of cancer growth andmigration (215) can then be offered the physician. This model has theadvantage that the different mechanisms of cancer spread can be turnedon or off in the simulations giving a spread of recurrence estimatesfrom the worst case to the less ominous. The model and its parameterscan be updated (225) on a continual basis based on observations andimaging of the patient (220) to provide a current best estimate tumordispersal map for planning of therapies.

Primary brain tumors are unlikely to spread distally by proliferation.Thus, the model will likely account for the spread due to bulkdissemination alone. If proliferation data is available and consideredimportant, these can be used. We point out that in the presence ofedema, such as in brain tumors and in injury, the influence of increasedextracellular volume fractions is profound. We illustrate this below.

The expansion of the extracellular space can greatly facilitatetransport of large particles such as glial tumor cells. For purelyillustrative purposes, consider a square lattice with lattice pointsspaced by d≧2, with circles of radius unity drawn at the lattice points,the area fraction of the lattice not enclosed within the circles is

$\begin{matrix}{\varphi = {1 - \frac{\pi}{d^{2}}}} & \left( {{Equation}\mspace{14mu} 17} \right)\end{matrix}$

(so that when the circles are just touching, φ≈0.215). Then the radius ρof the circle that can be accommodated within the 4-cusped regionsoutside the circles is

$\begin{matrix}{\rho = {\sqrt{\frac{\pi}{2\left( {1 - \varphi} \right)}} - 1}} & \left( {{Equation}\mspace{14mu} 18} \right)\end{matrix}$

The size (radius) of this circle increases from about 0.41 for theclosely packed case, when the originally considered circles just touchto about 1.5 when the volume fraction increases to 0.75. If the radiusof the original circles (the width of a myelinated axon for example) isabout 2 microns then the curve below suggests that a cell of radiusabout 1.5 times that, or about 3 microns can pass freely through theinterstitial spaces at volume fractions of 0.75. Such volume fractionsare of the order of magnitude of what has been observed in porcinebrains, and can be expected to occur in humans. Of course, cells beingdistensible do not need free passage to make it through interstitialspaces in even a passive way. The movement of distensible cells can beestimated through methods involving extensional shear and associatedforces that push the cells along the pathways of the flow of the fluid.FIG. 2A illustrates a radius of free circular area in extracellularspace (ECS) versus extracellular volume. Thus, when the brain is undernormal conditions, the extracellular volume fraction is at the origin ofthe abscissa, i.e. about 20% of the volume of, say tissue in whitematter, is extracellular. If we take the radius of an axon or fiber inthis space at 1 micron, then the spaces between axons, in the directionsof the fibers can accommodate a sphere of at most about 0.45 microns(the intercept of the curve with the ordinate). However, when, as is thecase with tumor-induced edema, the extracellular volume fraction canreach 70% or so, then the sphere that can be accommodated (say a cancerstem cell or cancer cell without appendages) can be well over a micronin radius, an increase of a factor of 3 in the linear dimension of theparticle that can be accommodated, and that can be transported withoutundue hindrance or need for distension of the cellular particle. Sincecells are quite distensible, this further increases the size of theparticles that can be transported due to the convection of ISF.

FIG. 3 illustrates how a radiation therapist can utilize the methods andsystems described herein for brain tumors, according to one embodimentof the invention. An overlay of high risk recurrence zones is providedfrom the tumor dispersal model (200 which is the output of FIG. 2) withthe radiation therapy (RT) map (305). Those skilled in the art canrealize several possible displays of risk of recurrence based on thecalculations of the model, including color coding, or contour maps. Theradiation therapist or physician then can make decisions based on thenew information available to her. Some of the processes that thephysician would go through are indicated in 310-340. Current radiationtherapy (RT) practice surrounds the contrast-enhancing mass in aGd-labeled MR acquisition with a margin of 1-2 cm., according tophysician judgment. This “ellipsoidal” region can be the target for RTtreatment. In one embodiment, information would be presented to thephysician that would display likely zones of recurrence of brain cancerfrom migration of the primary cancer cells, as already described inconjunction with FIG. 2. This is presented to the physician in aclinically useful two- or three-dimensional display (310). Furtherevaluation of these likely zones of recurrence will often be called for.Thus, depending on the status of the patient, the likely prognosis aftertreatment, or without it, decisions can be made regarding whether toirradiate regions which may seriously impact the quality of life of thepatient (330) or whether to attempt to treat white matter regions whichare known to be radiation resistant, or to defer these to surgery orchemotherapy (320). Based on this further information and evaluation, aRT plan for the patient may be constructed (325, 335). The RT plan mythen proceed (340).

FIG. 4 illustrates a process similar to FIG. 3, which can be utilized bya surgeon as part of the process of surgical resection of tumors. Theoverlay (410) of zones for high risk of tumor recurrence (200) with thecurrently available surgical plan (405) can be evaluated by the surgeonto make decisions, as mentioned in the description of FIG. 1A. 410-430are illustrative of some example decision processes the surgeon mayundergo. Current surgical practice can be rather uniform in its approachto treating patients. For example, since malignant glioblastomas areoften fatal, surgery can be generally prescribed if the tumor region isin an area with successful surgery rates. However, chemotherapy can beused instead to allow the patient to proceed with their remaining life(which sometimes is only weeks or months) without having the risk of amuch altered quality of life. Thus, in one embodiment, a physician canassess differences amongst such cases. As discussed in the text above,the physician can begin with a risk assessment for cancer migrationbased on the invention (410). One case may well involve a very low riskof cancer spreading throughout the brain and beyond, in which aggressivesurgery may be decided upon (430). Another may indicate that the diseasehas spread very considerably, in which case other avenues may be pursued(420, 425).

FIG. 5 illustrates a model- and patient image- and data-based map ofpathways of deposition of plaque in Alzheimer's, according to oneembodiment. In 501, radiological images of the patient are obtained. Acareful delineation of perivascular (and/or the Virchow-Robin spaces) isobtained in 502. Those skilled in the art will realize this isobtainable from arterial imaging such as angiography, both in CT and MRmodalities, arterial spin labeling (which does not require the invasiveinjection of a contrast agent), or other methods. These will provide, incombination with delineation of the sulcal grooves and the regionsoccupied by CSF (the ventricles, and in the sub-arachnoid space), adetailed map of the low pressure intracranial regions. Based on what isknown of the etiology of the disease and state of the art imaging onpatients, the primary cortical regions of formation of plaque (503) willthen be input into the flow model (100) to provide the most likelypathways for deposition of the plaque. Since the production is cortical,and the CSF spaces closest are often the perivascular, these willprovide the more likely regions toward which the plaque will migrate(rather than the deeper ventricular regions). This model (505) will thenbe presented to the neurologist or physician to determine treatment andprognosis (510).

FIG. 6 illustrates a bulk flow model as an inventive component of amodel for stem cell migration, both introduced and endogenous, in thepresence of injury or disease, according to one embodiment. In injury,there is significant edema and a consequent increase in extracellularvolume, as discussed above. This insight removes an obstacle to theunderstanding of the observed stem cell migration to sites of injury.Under normal circumstances, morphogens do not move more than severalcell diameters. A rough order of magnitude estimate can be arrived atfrom dimensional analysis alone, since the distance scale would be set,absent other factors, by the diffusion coefficient D of the morphogen,and its half-life τ. Then the distance scale one can arrive at would beL˜√{square root over (Dτ)}. Assuming, generously, D˜10⁻⁶ cm²/sec andτ˜10⁴ sec, L˜1 mm. This is hardly enough to account for migration ofcells across hemispheres. Thus, the more efficient process of bulk flowas described above can transport such cytokines over large enoughdistances to be sensed by remote stem cells. The movement of the stemcells can then be estimated by computed concentrations of the cytokines.

Returning to our description of FIG. 6, imaging (610) such as describedfor FIG. 1 can provide a detailed map of extracellular volumes (620).The injury is then the source of chemo-attractants and cytokines (suchas the stem cell factor (SCF)), and the flow model (100) provides arelative concentration map (in time and space) of such cytokines whichare the direction cues for stem cell migration (630). This model can beaugmented by diffusive transport and metabolic degradation (thesestrongly affect the detailed concentration profiles, but have far lessimpact on the convective wavefronts or pathways populated by thechemo-attractants). The known locations of the introduced or endogenouscells in the brain can also be input (633). Cell movement can also beinput (631). In 640, the model can then be a diffusive-convective modelwhich accounts for what is called “chemotaxis” of the cells, whichdrives them toward the injury source, and the retardation of thismigration due to the bulk fluid flow, which, of course. proceeds in theopposite direction, being the primary pathway for the dissemination ofthe chemo-attractants. Such an updated pathways map for stem cellmovement (650) has many uses in science and medicine. The field of braincancer stem cells is in its infancy. These are known, at least inpatients with brain tumors, to have residence sites in thesub-ventricular zone, in the dentate gyrus of the hippocampus, and incertain regions of sub-cortical white matter. It will be apparent to anyskilled in the art that if knowledge develops of any chemo-attractantsfor such cells, that the bulk flow and other dissemination of suchcytokines can be used to predict likely patterns of spread of braincancer stem cells.

Injection of an MR label at the injury site and/or labeled stem cells(625), estimates of chemo-attractant and/or stem cell pathways (635),and updated flow model(s) (645) can provide a method and apparatus bywhich these pathways are experimentally obtained. This alternativeroute, being invasive, can be exploited more easily in animals, but inany case can also be used in conjunction with the pathways of cellmovement model (650) to provide continual refinements and updates.

FIG. 7 illustrates a chemotherapy delivery model 700, according to oneembodiment. In the previous figures, we describe bulk endogenous flowand convective transport of particulate matter due to such flow. FIG. 7provides estimates of the distribution within brain parenchyma ofsystemically introduced particles. FIG. 6 explored endogenous flow. Thisallowed us estimates of the distribution of particles residing in thebrain parenchyma, be they endogenous or introduced for therapeutic ordiagnostic reasons. As in FIG. 6, one or more radiological images areobtained. For systemically introduced particles, we need to estimaterates of ingress into, and egress across the blood vessels from, brainparenchyma. Thus, a map of key anatomical characteristics of the bloodsupply (710) is utilized including the density of the blood vessels andtheir permeability to molecules introduced in a standard way inperfusion imaging. These can include both MR markers (such as Gd-DTPA)or CT markers. Those skilled in the art can supply a variety of otheravailable methods. The model then employs known scaling estimates, orin-silico measurements to infer the permeabilities and residence timesfor water soluble proteins of the desired molecular weight. The use ofdynamic contrast enhanced imaging (DCE) to construct the parametersrelevant to transcapillary exchange have been described above in thesection pertaining to DCE and are captured in 715. If thechemotherapeutic molecule is instead lipid-soluble, similar derivedestimates from the body of biological research or measurements onavailable testbeds can be used. However, in this case, scaling fromin-vivo measurements from Gd-DTPA are not relevant, since lipid-solublemolecules actively diffuse through the lipid bilayer of the cellsconstituting the BBB, unlike the water soluble ones to which the BBB isa semi-permeable membrane with barriers alternating with water channels.In either case, based on such estimates, we construct a trans-capillaryexchange model (720). This, with information about the chemotherapyprotocol (722), provides a source term for the entry and the rate ofentry of the chemotherapeutic molecule into the parenchyma. The flowmodel (100) then allows us to create a chemotherapy delivery model (712)and estimate the chemotherapeutic profile and residence time in brainparenchyma. An alternative path would be to observe selected points inthe brain for the concentration of the molecule by micro dialysis orother means. A neural network or other statistical estimator can then beused to predict the distribution profile over the entire parenchyma. Itsaccuracy will depend on the number and distribution of the microdialysis probes, and of the amount of a priori information, such as themodel just described, that is available to the statistical estimator. In730, 735, and 470, we illustrate another embodiment that can worksynergistically with the model construction mentioned above. With theintroduction of a substance (730), (such as microdialysis probes, asmentioned), we can follow the concentration of the introducedchemotherapeutic agent (735) in brain parenchyma. The results of thesemeasurements can, in a loop familiar from optimal control theory, bemade to influence parameters of the model for a better fit to the data(740). We now describe one theoretical construction of a chemotherapydelivery model.

Chemotherapy Model Mathematical Equations.

For the chemotherapy delivery model, we begin with writing down theequations describing the concentration n(x, t) of the chemotherapeuticmolecules. (Usually we suppress the space and time arguments). This iscompletely analogous to the equations for the albumin and the tracerabove

$\begin{matrix}{\frac{\partial n}{\partial t} = {{\nabla{\cdot ({vn})}} + {\nabla{\cdot \left( {D_{n}{\nabla n}} \right)}} + q_{n} - {k_{d}n}}} & \left( {{Equation}\mspace{14mu} 21} \right)\end{matrix}$

Note that v is the bulk flow velocity, n are the concentrations, D_(n)is the diffusion tensor of chemotherapeutic molecule, k_(d) is thecoefficient rate of degradation, and q_(n) is the interstitialproduction rate. Thus, the terms on the right hand side represent, fromleft to right, the convective transport in the interstitium, thediffusive transport therein, the transcapillary transport, and finallythe irreversible degradation, metabolism, etc., in the parenchyma.Obviously, we have linearized the last term. We repeat the equations fortranscapillary transport

$\begin{matrix}{{q_{n} = {{\frac{{PS}_{n}}{V}\left( {n_{v} - n} \right)} + {{q\left( {1 - R_{n}} \right)}n_{v}}}}{{\varphi_{v}\frac{n_{v}}{t}} = {{F\left( {n_{A} - n_{v}} \right)} - {\frac{{PS}_{n}}{V}\left( {n_{v} - n} \right)}}}} & \left( {{{Equations}\mspace{14mu} 22},23} \right)\end{matrix}$

The chemotherapy molecule-specific parameters are now labeled by thesubscript n. Note that n_(v) is the concentration in the blood vessels,n_(A) is the arterial input function,

$\frac{{PS}_{n}}{V}$

is the permeability area production for the unit tissue volume, F is theregional cerebral blood flow, and φ_(v) is the volume fraction of tissueoccupied by blood vessels. In the first of the equations just above, theflow rate per unit volume of tissue has the usual terms due toconcentration-driven transport, and convective flow across the capillarywalls. We recall that, strictly speaking, R_(n) should not be labeled anosmotic reflection coefficient, but rather a solvent drag orultrafiltration coefficient. However, it does not appear in otherequations so there is no risk of confusion here. The second equation issimilar to that used in DCE (chemotherapy is a very similar processafter all). The equation for q, the transcapillary transport of water,can be assumed to be entirely unaffected by the chemotherapeuticmolecule so that the osmotic reflection coefficient of the serum albuminproteins alone will enter into it.

We have already discussed the estimation of the bulk flow velocity v,the cerebral blood flow F, and the plasma filtration rate q above, so werestrict our attention here to methods of estimation of the remainingparameters. These are

$\frac{{PS}_{n}}{V},$

n_(A), and R_(n). (We assume that degradation rates are available frompharmacokinetic sources. One example use of the model will be indetermining effective coverage of the chemotherapeutic molecule, inwhich case the long term distribution of an unmetabilized molecule isnot of much interest. Thus, the solution for short times with thedegradation rate set to zero is of considerable practical interest.) Thepermeability and the reflection coefficients are sensitive to theultrastructure of the capillaries, and their variation is important inunderstanding the effects of the blood brain barrier disruption can bedetermined by known scalings from the values determined for the tracermolecule. Selection of tracers of similar molecular weight, size, andsolubility in water/oil to the chemotherapeutic molecule is to bepreferred. However, the literature provides scaling relations formolecules of different size: permeability of globular water solublemolecules tends to be proportional to

$\frac{1}{\sqrt{MW}},$

where MW is the molecular weight, until a certain size, and for a fixedoil/water partition coefficient, and more sophisticated relations anddata are available. n_(A) is determined from the injection protocol.

FIG. 13 illustrates an example of a chemotherapy model, according to oneembodiment. shown for ease of display in two dimensions (although threedimensions can also be displayed), the chemotherapy model can exhibit acolor coded display of the concentration of a chemotherapeutic moleculein selected two dimensional planes. FIG. 13 illustrates pictures ofaxial slices positioned at different levels along a vertical axis. Thecolor code (white is hot or high, and the cooler colors are lowintensities) shows how much of a drug there is at a given time. On theleft of FIG. 13 is a graph that shows the corresponding time (in hours,on the abscissa of the graph) as well as the concentration of the drugin the bloodstream. Illustrations such as those showed in FIG. 13 canhelp in devising chemotherapeutic plans for a patient, and themethodology described herein can take into account the physiologicalstate of the patient such as the status of the blood brain barrier.Different time points are shown in the different images.

FIG. 14 shows an example of a migration illustration, according to oneembodiment. The high risk zones for cancer recurrence are displayed asan overlay on a radiological image (the image on the right of FIG. 14).More refined displays, color coded according to the likelihood forrecurrence, may also be envisaged. The spread can be filamentous andquite dependent on direction, as shown in FIG. 14.

FIG. 8 is a flowchart illustrating RT and chemotherapy integration,according to one embodiment. The BBB permeability is alterable either asa (usually not desired) by-product of treatments such as radiationtherapy, or of the deliberate introduction of BBB altering agents.Further systemic introduction of molecules accounting for the newlydisrupted BBB can be used along with any consequent edema (810), by acombination of methods already discussed with respect to FIGS. 1-7. FIG.8 shows that a particular application of this process and apparatus canbe the integration of RT (300) and chemotherapy (700), by taking“advantage” of the increased BBB permeability (820) as a result of RT.In 825, a database and data-driven model can be built for theRT/chemotherapy integration. Another application is to just exercise thechemotherapy delivery model described in FIG. 7, but after theintroduction of a BBB altering drug.

FIG. 9 describes a process in which the system and method can be used asa part of the pharmaceutical drug development process, according to oneembodiment. The data collected during early phases of the drugdevelopment process (pharmacokinetics and so on, 905) along with theinitially estimated desired dose (according to the expected response,915) is made available as input. As previously described, a profile canbe provided of the expected disposition of the agent in brain parenchyma(935). This allows for an iterative refinement of the delivery plan(945) with inputs from the known or estimated dose-response curves (950)which are allowed to be dependent on the disease state of the tissuewhere desired responses are hoped for.

We note that, in one embodiment, an optimal delivery plan can begenerated. We can start with a reasonable first guess for a deliveryplan, and based on the desired dose and spatial distribution of thedose, we can alter the delivery parameters within a range. Those skilledin the art will know how to quantify the match of the expected dose tothe desired, and thus obtain an “optimal” plan. The variation of therange of delivery parameters can be done at first crudely over largeintervals, and then successively refine the intervals to obtain anoptimal delivery plan.

We can also integrate advances in molecular imaging as they becomeavailable and are desired to be used, to refine the model from the useof current pharmacokinetic data usually obtained in cell cultures, toin-vivo kinetics (955) that is beginning to be available in researchlaboratories, and will be increasingly available in routine clinicalpractice. This can, in turn, lead to more refined delivery plans forpatient-specific optimization (960). The model used by itself, or inconjunction with these forms of molecular imaging will result in detailsof the spatial patterns of drugs as they distribute in a living brain(965) which will result in increased utility to the pharmaceuticalindustry.

FIG. 10 illustrates example uses of the methods and systems describedherein as services to select industries. In particular the continual useof the processes described herein (e.g., flow model 100, chemotherapymodel 700) will be enhanced by access to, and performance of,radiological imaging on a single patient over time, i.e. longitudinally(1005). These can all be combined into an integrated model (1010). Thisintegrated model can be used in many circumstances. For example, anin-vivo estimate of intracerebral pressure variations from imaging(1030) could be of utility as software module in existing scanners andthus of application interest to radiological imaging suppliers. Researchand other hospitals could also be interested in some of these componentsapart from their integrated use in patient care as described in theprevious figures. We have described in detail the development and use ofa chemotherapy model in the simulation of chemotherapy delivery. It canbe envisaged however, that outputs of such a model, such as thefunctional capillary density, may be used for diagnostic purposes inbrain cancer. Such an application could be used in functional capillarydensity predictions (1015). Similarly, diagnostic and other applicationscan be envisaged for quantification of blood-brain barrier disruption(1025) or cerebral blood flow (1020). Such applications can also beprovided, with methods of display that enhance the clinical utility ofthe numerical estimates (see below).

User Interface

In one embodiment, a method and system are provided for numericalmodeling of the motion of materials (e.g., endogenous and/ortherapeutic) in the setting of the human brain as has been detailedabove. Extending the usage of microscale and nanoscale to all the metricprefixes, anatomy emphasizes the centiscale and deciscale: This range isreferred to as the anatomical scale. Anatomy represents a distinct kindof understanding, with a strong emphasis on characterizing whole tissuesby their geometrical and functional relation to their surroundings andthe rest of the body. In one embodiment, the microscopic processes oftransport are addressed, from molecules to migrating cells, with anemphasis on the role of bulk endogenous flow, particularly when there isinjury and consequent expansion of the extracellular spaces. The modelcan account for the influence of porosity, tortuosity, and othermicroscale features while drawing on milliscale data from 3D scanning(e.g., CT for anatomical detail, MR for concentration and diffusiontensor estimation, edema) to construct and solve appropriate partialdifferential equations (PDEs). Scalar or tensor values can be provided,distributed in space with features such as a point of maximumconcentration, but without sharp boundaries. In one embodiment, thesemodels can predict and improve the targeting of drugs across theblood-brain barrier, and predict the spread of cellular material withinthe brain. In addition, in one embodiment, these models can be clearlydisplayed and used. Thus, a clinician can select a protocol in a seriesof cases, predict the outcome, and compare it with outcomes clinicallypredicted for other options. If, in a substantial proportion of cases, abetter outcome appears available than with the clinician's choice, andthe prediction of this better outcome has a substantial degree ofconfidence, then the potential for clinical improvement exists.

It should be noted that the clinicians' predictions can be improved ifthey can theorize as a researcher. A researcher can predict outcomes forother protocols chosen with complete freedom, allowing multiple attemptsand inspection of details via close familiarity with the workings of themodel. For example, a researcher could determine that there is not muchmigration to the lesion, but what migration there is appears to be via acertain edematous region, so the researcher could theoretically move theinjection site to other regions, which is upstream of the edema in CSFcirculation. Clinical utility is thus assisted by an interface whichmakes such exploration fast and effective.

In one embodiment, data from PDEs is extracted to create a networkrepresentation of the brain's transport properties for the materialconsidered, summarizing and approximating them by a 3D structure ofcurves joining nodes. This assists in multiple purposes: ‘lumped’approximate computation, clear visualization, effective interaction andplanning, an explicit relation with anatomical concepts, etc. The curvesand nodes of the model make anatomical sense and can allow automatedanatomical labeling.

This comprehensible and anatomically meaningful representation of vitalprocesses in the brain, from the perfusion of a drug to the migration ofstem cells and metastasizing tumor cells, can create new anatomicalunderstanding by empowering thought about the interaction betweenstructure and process dynamics. The transport network representationacts as a mental and computational bridge between anatomy, on the scaleof the brain in the large, and detailed transport biophysics modeled onthe nano- and microscales and computed on the milliscale. Both as adescriptor of transport in the ‘general brain’ and in patient-specificinstances, where the representation is built afresh from patient data,it can lead to new levels of understanding of the dynamic relation amongthe brain and its parts.

Creating a Detailed Display of Brain Tissue

High description of tissue gives not merely its shape and position, butits function, and clinically all of these must be patient-specific. Wehere address the extraction of structured information at a high level,arising from work with data gathered and handled on a milliscale grid,and modeled by equations structured by our knowledge of processes on themicro- and nanoscale, such as flow through a medium with tortuous pores,and cellular take-up of materials.

For clinical use, software exploiting our algorithms can display resultsat the centiscale and even the brain-spanning deciscale. The anisotropyof flow in the brain gives rise to pseudochannels described in moredetail below, defined as curves along which maximal effective transport(a maximum eigenvalue cmax of the relevant tensor) is greater than alongall neighboring curves. Such a curve is most channel-like when cmax mostexceeds the other eigenvalues, but the definition generically givessmooth curves wherever the larger two eigenvalues are distinct.(Equality combined with the maximality conditions gives branch points,and hence nodes in the network.) This can thus support a powerfullyannotated network view when choosing injection points, and a basis forpatient-specific network models.

The channel extraction logic can directly map mechanical transportproperties; but nerve bundle geometry, with long extracellular spacesbetween closely packed cylindrical axons, can show the major neuralpathways as pseudochannels. We thus can identify major nerves, usinganatomical referents to identify which nerve is which and thus topresent them as named top-level structures connecting with the largebody of knowledge that exists at this level rather than at finer scales.In particular, this can allow software to warn when a surgical plan(pre- or intra-operative) comes dangerously close to one of these keystructures.

Since so many of the brain's processes consist of or involve signaling,at a range of speeds from the nerve impulse to the migration of stemcells and metastasizing tumor cells, we are thus providing thefoundations for a systematic functional map, firmly rooted in individualrather than average or idealized brains, and for software that will useit in practical planning assistance to the clinician (e.g., surgeon).

In one embodiment, a systematic digital embodiment of the relationbetween the large-scale structure of the brain is provided, includingmany functional properties, and the scale at which it is practical tocompute material transport, which in turn involves cellular and membraneprocesses best understood on the micro- and nanoscales.

In one embodiment, a system and method are provided for creating arepresentation of (modeled) transport properties of the brain which istransparent and usable to the clinician. Density fields with fewdiscontinuities are both hard to display clearly, and hard to thinkabout. The clinician knows far more of the patient's brain anatomy,physiology, localization of function, eloquent regions, sensitivity toinvasive trauma, and so on than can be embedded in current software. Ourschema extracts from the field data of the PDEs in the model a networkrepresentation of the brain's transport properties for the materialconsidered, summarizing and approximating them by a 3D structure ofcurves joining nodes. This will be valuable for multiple purposes:‘lumped’ approximate computation, clear visualization, effectiveinteraction and planning, and an explicit relation with anatomicalconcepts. The curves and nodes make anatomical sense and in many casesallow automated anatomical labeling. The curves can be constructed forthe transport of any material of interest, from small molecules tocells. In some embodiments, we expect (anatomically) a great deal ofcommonality, but not identity, between the networks constructed fordifferent materials. Any curve that appears in all or most of them (inthe sense that in each network a curve can be chosen that is a goodapproximation of a corresponding curve chosen in another network), willusually correlate with an important anatomical structure.

The idea of flow along a curve, even a curve in three dimensions, is ofcourse a simplification. Real materials move as evolving concentrations,as reflected in our equations. (Even at the particle level, shared pathsexist only statistically.) However, material transport in the brain hasphenomenological paths of some importance. For example, there is thepseudochannel, any narrow region for which transport is easier along itthan either across it or along nearby curves in the same direction. Apseudochannel tends to capture a large part of any flow that is activein the volume it lies, and is a feature of the three-dimensionallandscape. We can quantify this idea by defining the core of apseudochannel as a curve along which the greatest effective diffusioncoefficient cmax (an eigenvalue of the EDC tensor) is greater than atany nearby point in the directions belonging to the lesser eigenvalues.This may be illustrated in the plane by the tensor field (which is infact the Hessian of [(1+r cos(3θ))r2/2+r4], though not every symmetric 2tensor arises from a scalar field). FIG. 11 shows strong eigendirections in black, weak ones in gray. The core C consists of pointswhere the large eigenvalue cmax is greater than at ‘sideways’neighboring points. (In general cmax also varies in its own direction,and requiring maximality there would give us isolated points.) At pointswhere the eigenvalues—in 3D, the two greatest eigenvalues—are equal, thecurve branches. FIG. 11 includes a generic example. The types ofbranching may be classified by means analogous to those in modernmathematics of the differential geometry of curves and surfaces, and thecorresponding use of higher expansion coefficients leads to effectivenumerical siting of particular instances. Branch points give rise tonodes in the network of core curves.

In constructing a network we will use a combination of fine-scale andlarge-scale criteria to prune off clutter. A short side branch that goesnowhere, and has cmax values that are only gently greater than the othereigenvalues at each point of this side branch, or are unsharply maximalacross it, will be discarded. Even a numerically weak segment thataffects the overall connectivity of the network will be retained.

Strictly, the definitions here involve tensor fields and differentiationdefined on an infinitely divisible continuum with no characteristicdirections of its own (as distinct from anisotropy of the fields), whileour computations are on a discrete rectangular grid at the milliscale.

For a thin channel the decrease through neighboring curves is rapid, sothat transport will be concentrated in a pseudochannel P around C. Thisdoes not have sharp borders, but we approximate an effective thicknessfrom the size of quadratic coefficients in the Taylor expansion of cmaxacross C. Combined with the directional coefficient cmax itself, thisgives an approximate transport coefficient along the pseudochannel ateach point on C, which can be integrated by ‘in series’ logic to give asingle lumped channel capacity number for each curve segment betweennodes. This allows rapid, approximate calculations of total transportthrough the brain, on the anatomical scale: We can tune the channelcapacity estimator and the channel transport dynamical equations for thebest agreement we can reach with the milliscale PDE solutions that givemore accurate results. They can thus support an overview navigationsystem through the PDE model. We can display a network of 3D channelscolor-coded for cmax value, thickness and approximate capacity.Superposed on translucent brain anatomy, this provides a powerfully andinteractively annotated view when choosing injection location, pressureparameters, etc. Expected network transport can be computed and updatedin real time as the user moves a choice, and the channel view will givestrong cues as to what direction to move for improved results (both inincreasing delivery to a target, and in reducing it in tissuesvulnerable to side effects). Choices can be checked and fine tuned byinvoking the milliscale model, but the interactive process of using thesimulation can be greatly strengthened by comprehensible display oftransport behavior at the anatomical scale.

In one embodiment, the network thus constructed from milliscaletransport data is not merely visualizable on the anatomical scale, butmeaningful at this scale. The anisotropies of transport are notanatomically arbitrary, but arise from structure. For example, a majornerve is a closely packed bundle of near-cylindrical axons; away fromcell bodies, such assemblies tend to arrange themselves hexagonally, asshown in FIG. 12, so that the extracellular transport medium occupiesthe long spaces between them. Even with the irregularities of real cellassemblies, averaging gives to the transport coefficient tensor for mostmaterials a largest eigenvalue direction aligned with the bundle. Otheranatomical features such as the inner folding of the cortex (as distinctfrom the outer folds, or sulci, outside the blood-brain barrier), alsoimpact transport properties. A ventricle is visible in various imagingmodalities: it acquires transport anisotropy only by forced or naturalflow of the cerebrospinal fluid they contain, but where narrow on thescale of averaging used in diffusion tensor scanning, the resultingfield is anisotropic. This must be recognized and connected to theventricle as a distinct class of object in the transport network. We cananalyze carefully the relation of all these features in the primaryscans on which we build and test our system, first identifying theanatomy involved in each branch of the pseudochannel network, thenautomating as far as possible the recognition process in new data, forthe more reproducible segments and nodes. The resulting anatomicallyannotated transport map can have a more direct relation to the mentalframework of the practicing surgeon or radiologist than a visualizationof intensities alone can accomplish. Moreover, as the normal range oftransport maps becomes apparent through use with multiple patients,abnormalities may become highly recognizable to the human user. Sincetransport is a fundamental process in the brain, this could provide animportant new diagnostic tool.

For an actual computed or measured transport we can define thestreamlet, similarly defined from the flow field and visualizing theflow more clearly than is easily achieved with a density map in 3D. (Ina plane an animated map of levels, smoothly color-coded rather thanshown by level contours, shows flow very clearly. Visualizing smoothscalar variations in 3D space is far more difficult.)

In one embodiment, software can be constructed as follows: (1) Anumerical definition of pseudochannels can be provided. Numericalalgorithms can be built for the identification of maximal-eigenvaluecurves, applied to the measured diffusion tensor and to transport-tensorfields constructed numerically using biophysical model equations. (2) Anumerical definition of pseudochannel nodes can be provided. Where twoeigenvalues are co-maximal relative to those at nearby points, theassociated curves generically branch. Such points can be identifiednumerically and characterize the branching directions. (3) Ventriclescan be characterized. Ventricles can be identified from scan data andtheir transport properties can be quantified. (4) Construction of a 3Dpseudochannel network can take place. Ventricles and pseudochannelcurves and nodes can be assembled into an object oriented model of agraph embedded in three-dimensional space. (5) A streamlet network canbe constructed. Given a specific flow field, derived from experimentaldata or tracked transport, the above algorithms can be used to create auser-understanding-friendly ‘sketch’ of it, as a graph analogous to thepseudochannel network. (6) Lumped network dynamics can be optimized.Pseudochannel ‘thickness’ can be quantified as a measure inverse to howsharply peaked it is relative to neighboring maximal-eigenvalue curves,and a lumped ‘channel capacity’ can be derived to be associated withtransport between the nodes it joins. This characterization and a modelof flow dynamics can be tuned along the network, for best agreement withnumerical solutions of full partial-differential-equation (PDE) flow inthe underlying tensor field from which the network was derived. (7)Network elements can be anatomically identified. Anatomical comparisoncan be used with patient scan data to identify some pseudochannels andnodes with named brain features such as nerve bundles and portalsystems. Algorithms can be created to automate such identification innew patient data. (8) The visual setting of the brain can be displayedin a 3D display. An interface can be created by which a user can see therelation of the network to a translucent volume display of a scannedbrain, with channel properties coded by color and geometric thickness:The cognitive value and immediacy of different coding schemes can beexplored. Numerical experiments can be enabled with user placement of abolus of material for transport and display of results from both thenetwork model and the finer-scale PDE model.

CONCLUSION

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample, and not limitation. It will be apparent to persons skilled inthe relevant art(s) that various changes in form and detail can be madetherein without departing from the spirit and scope of the presentinvention. In fact, after reading the above description, it will beapparent to one skilled in the relevant art(s) how to implement theinvention in alternative embodiments. Thus, the present invention shouldnot be limited by any of the above described exemplary embodiments.

In addition, it should be understood that any figures, screen shots,tables, examples, etc. which highlight the functionality and advantagesof the present invention, are presented for example purposes only. Thearchitecture of the present invention is sufficiently flexible andconfigurable, such that it may be utilized in ways other than thatshown. For example, the steps listed in any flowchart may be re-orderedor only optionally used in some embodiments.

Further, the purpose of the Abstract of the Disclosure is to enable theU.S. Patent and Trademark Office and the public generally, andespecially the scientists, engineers and practitioners in the art whoare not familiar with patent or legal terms or phraseology, to determinequickly from a cursory inspection the nature and essence of thetechnical disclosure of the application. The Abstract of the Disclosureis not intended to be limiting as to the scope of the present inventionin any way.

It should be noted that the phrase “comprising . . . a” throughout theclaims means “comprising . . . at least one”.

Furthermore, it is the applicant's intent that only claims that includethe express language “means for” or “step for” be interpreted under 35U.S.C. 112, paragraph 6. Claims that do not expressly include the phrase“means for” or “step for” are not to be interpreted under 35 U.S.C. 112,paragraph 6.

1. A method for providing information regarding administration of achemotherapy treatment for neurological disease in a patient,comprising: obtaining radiological imaging from the brain of the patientfollowing systemic administration of an agent into the brain; obtainingserum concentration level information of the agent; determining centralnervous system tissue concentration level information of the agent, thetissue concentration level information accounting for blood-brainbarrier state information, chemical property information, and physicalproperty information of the agent; obtaining other physiologicalinformation from radiological imaging and/or clinical data; displayingthe radiological imaging, the serum concentration level information, thetissue concentration level information, or the other physiologicalinformation, or any combination thereof, in a chemotherapy model.
 2. Themethod of claim 1, wherein the tissue concentration level information isdisplayed as: a 2-dimensional illustration, a 3-dimensionalillustration, an intensity illustration, a color-coded illustration, astatic illustration, or a dynamically altering (with time) illustration,or any combination thereof.
 3. The method of claim 1, furthercomprising: making available the tissue concentration level informationfor data analysis.
 4. The method of claim 1, wherein the chemotherapymodel also takes into account retrospective data on the behavior of theagent.
 5. A system for providing information regarding administration oftreatment for neurological disease in a patient, comprising: a servercoupled to a network; a user terminal coupled to the network; anapplication coupled to the server and/or the user terminal, wherein theapplication is configured for: obtaining radiological imaging from thebrain of the patient following systemic administration of an agent intothe brain; obtaining serum concentration level information of the agent;determining central nervous system tissue concentration levelinformation of the agent, the tissue concentration level informationaccounting for blood-brain barrier state information, chemical propertyinformation, and physical property information of the agent; obtainingother physiological information from radiological imaging and/orclinical data; displaying the radiological imaging, the serumconcentration level information, the tissue concentration levelinformation, or the other physiological information, or any combinationthereof, in a chemotherapy model.
 6. The system of claim 5, wherein thetissue concentration level information is displayed as: a 2-dimensionalillustration, a 3-dimensional illustration, an intensity illustration, acolor-coded illustration, a static illustration, or a dynamicallyaltering (with time) illustration, or any combination thereof.
 7. Thesystem of claim 5, wherein the application is further configured for:making available the tissue concentration level information for dataanalysis.
 8. The system of claim 5, wherein the chemotherapy model alsotakes into account retrospective data on the behavior of the agent.
 9. Amethod for providing a representation and display of brain physiologicalinformation, comprising: obtaining radiological imaging correlates of aphysiological state of the brain; obtaining a constitutive property ofthe brain; constructing a network representation of the constitutiveproperty and any corresponding flow; and displaying the networkrepresentation with the radiological imaging as a pseudo-channel model.10. The method of claim 9, wherein the constitutive property includes atransport property, a tensor, capacity, or any combination thereof. 11.The method of claim 9, wherein the pseudo-channel model is a networkrepresentation of three dimensional curves joining nodes.
 12. The methodof claim 9, wherein the constitutive property is color coded.
 13. Themethod of claim 9, wherein the pseudo-channel model can be updated anddisplayed in real time as a user inputs additional information.
 14. Asystem for providing a representation and display of brain physiologicalinformation, comprising: a server coupled to a network; a user terminalcoupled to the network; an application coupled to the server and/or theuser terminal, wherein the application is configured for: obtainingradiological imaging correlates of a physiological state of the brain;obtaining a constitutive property of the brain; constructing a networkrepresentation of the constitutive property and any corresponding flow;and displaying the network representation with the radiological imagingas a pseudo-channel model.
 15. The system of claim 14, wherein theconstitutive property includes a transport property, a tensor, capacity,or any combination thereof.
 16. The system of claim 14, wherein thepseudo-channel model is a network representation of three dimensionalcurves joining nodes.
 17. The system of claim 14, wherein theconstitutive property is color coded.
 18. The system of claim 14,wherein the pseudo-channel model can be updated and displayed in realtime as a user inputs additional information.